The halo of the exotic nucleus 11Li: a single Cooper pair

Barranco, F.; Bortignon, P. F.; Broglia, R. A.; Colò, G.; Vigezzi, E.

doi:10.1007/s100500170050

Cited by 100 publications

(210 citation statements)

References 27 publications

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“…This applies, in particular, to the case of the s 1/2 state, which is unbound in our initial mean-field potential (cf . Table I), and is essential in the case of 11 Li [25].…”

Section: Be͑mentioning

confidence: 99%

Parity inversion and breakdown of shell closure in Be isotopes

et al. 2004

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The coupling of single-particle motion and of vibrations in 4 11Be produces dressed neutrons which spend only a fraction of the time in pure single-particle states, and which weighing differently from the bare neutrons lead to parity inversion. If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron saturated the nucleus expels most of the wave function of the last neutrons outside to form a halo, which because of its large size can have lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, solution which is on the basis of BCS theory of superconductivity. To understand the origin and the consequences of pairing correlations, it is illustrative to study the problem of two electrons interacting on top of a noninteracting Fermi sea of electrons. Thus, all but two of the electrons are assumed to be noninteracting. The background of electrons enter the problem only through the Pauli principle by blocking states below the Fermi surface from participating in the twoelectron problem.This system, first studied by Cooper [1], is unstable against the formation of a bound electron pair, regardless of how weak the interaction is, so long as it is attractive. This result is a consequence of the Fermi statistics and of the existence of the Fermi-sea background, since it is well known that binding does not ordinarily occur in the twobody problem in three dimensions until the strength of the potential exceeds a finite threshold value.Although actual superconductors differ in a fundamental way from a single bound pair model, Cooper pairs can be viewed as the building blocks of the superconductor. Furthermore, in the nuclear case, where the number of fermions participating in the condensate is small, and where the pairing problem can be studied in terms of individual quantal states, the Cooper pair problem can describe realistic situations. In fact it seems to have a concrete realization in the halo nucleus 12 Be͑ 10 Be+2n͒, which can be viewed as two weakly bound neutrons moving around the core 10 Be. By allowing these two neutrons to interact through the bare nucleon-nucleon potential, and to exchange surface vibrations of the core, one is able to provide a unified and quantitative picture of the observed properties of this system. This result, which is quite general, suggests a strategy for designing nuclei at the edges of the neutron drip line, and thus probing the limits of nuclear stability. It also provides evidence of the limits of validity of BCS theory in finite systems: a single Cooper pair.The properties of finite many-body systems are strongly influenced by spatial quantization [2] leading to marked shell structures [3]. This type of quantal size effects are, on the other hand, reno...

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“…This applies, in particular, to the case of the s 1/2 state, which is unbound in our initial mean-field potential (cf . Table I), and is essential in the case of 11 Li [25].…”

Section: Be͑mentioning

confidence: 99%

Parity inversion and breakdown of shell closure in Be isotopes

et al. 2004

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“…Although the dineutron structure as a consequence of the pairing correlation has been suggested for some time in 11 Li and 6 He nuclei [1,3], it is only recently that a strong indication of its existence has been obtained experimentally in the Coulomb dissociation of 11 Li [4]. The new measurement has stimulated lots of theoretical discussions on the dineutron correlation, not only in the 2n halo nuclei, 11 Li and 6 He [5,6,7,8], but also in medium-heavy neutronrich nuclei [9,10] as well as in infinite neutron matter [11,12].…”

Section: Introductionmentioning

confidence: 99%

Strong dineutron correlation inHe8andC18

2008

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We study the spatial structure of four valence neutrons in the ground state of 8 He and 18 C nuclei using a core+4n model. For this purpose, we employ a density-dependent contact interaction among the valence neutrons, and solve the five-body Hamiltonian in the Hartree-Fock-Bogoliubov (HFB) approximation. We show that two neutrons with the coupled spin of S=0 exhibit a strong dineutron correlation around the surface of these nuclei, whereas the correlation between the two dineutrons is much weaker. Our calculation indicates that the probability of the (1p 3/2 ) 4 and [(1p 3/2 ) 2 (p 1/2 ) 2 ] configurations in the ground state wave function of 8 He nucleus is 34.9% and 23.7%, respectively. This is consistent with the recent experimental finding with the 8 He(p, t) 6 He reaction, that is, the ground state wave function of 8 He deviates significantly from the pure (1p 3/2 ) 4 structure.

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“…The density variation then changes from normal nuclear density to an exponentially decreasing tail of the two neutrons. This interesting system was considered within BCS theory more than a decade ago (Barranco et al 2001).…”

Section: Crossover In Finite Halo Nucleimentioning

confidence: 99%

Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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Abstract. The experimental revolution in ultracold atomic gas physics over the past decades have brought tremendous amounts of new insight to the world of degenerate quantum systems. Here we compare and constrast the developments of cold atomic gases with the physics of nuclei since many concepts, techniques, and nomenclatures are common to both fields. However, nuclei are finite systems with interactions that are typically much more complicated than those of ultracold atomic gases. The simularities and differences must therefore be carefully addressed for a meaningful comparison and to facilitate fruitful crossdisciplinary activity. We first consider condensates of bosonic and paired systems of fermionic particles with the mean-field description but take great care to point out potential problems in the limit of small particle numbers. Along the way we review some of the basic results of BEC and BCS theory, as well as the BCS-BEC crossover and the Fermi gas in the unitarity limit, all within the context of ultracold atoms. Subsequently, we consider the specific example of an atomic Fermi gas from a nuclear physics perspective, comparing degrees of freedom, interactions, and relevant length and energy scales of cold atoms and nuclei. Next we address some attempts in nuclear physics to transfer the concepts of condensates in nuclei that can in principle be built from bosonic alpha-particle constituents. We also consider Efimov physics, a prime example of nuclear physics transfered to cold atoms, and consider which systems are more likely to show interesting bound state spectra. Finally, we address some recent studies of the BCS-BEC crossover in light nuclei and compare them to the concepts used in ultracold atomic gases. While many-body concepts such as BEC or BCS states are applicable in both subfields, we find that the interactions and finite particle numbers in nuclei can obscure the clear meaning they have in cold atoms. On the other hand, universal results from atomic physics should have impact in certain limits of the nuclear domain. In particular, with advances in the trapping of few-body atomic systems we expect a more direct exchange of ideas and results.

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The halo of the exotic nucleus 11Li: a single Cooper pair

Cited by 100 publications

References 27 publications

Parity inversion and breakdown of shell closure in Be isotopes

Parity inversion and breakdown of shell closure in Be isotopes

Strong dineutron correlation inHe8andC18

Comparing and contrasting nuclei and cold atomic gases

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